The Tynecastle skipper stepped up on his 29th birthday following a trip on Callum Paterson by Owain Tudur Jones.
The Welshman had earlier fired Inverness in front with his first goal for the club; a thunderous strike.
The late equaliser will provide some joy for Hearts in a week when they fell under the threat of a winding-up order over an unpaid tax bill.
Inverness, who are now 10 games unbeaten, remain third in the Scottish Premier League, having squandered the chance to join front-runners Celtic and Hibernian on 21 points.
Hearts, stay in 10th spot after a week of turmoil - again!
Financial problems at the club and a tax demand for almost £450,000 has put the club under threat.
Steve Kilgour, of the Federation of Hearts Supporters' Clubs, told BBC Scotland that fans should seize the chance to safeguard their future.
"We have to stand on our own two feet and it's imperative the supporters back the share issue," he told BBC Scotland.
Hearts hope to raise £1.79m with a share offer that will give supporters a 10% stake in the Edinburgh club.
"Vladimir Romanov is no longer financing the club or bankrolling it," Kilgour said.
"We need £2m to carry us through to the summer. Each season, there's a £2m deficit and we have to find that.
"That may come and go a bit if we manage to move players on in January."
Kilgour said it was time for the Hearts fans to stand up and be counted and he appealed to those supporters who bought tickets for glamour ties against Tottenham Hotspur and Liverpool to come forward.